Answer:
11.25
77.85
Step-by-step explanation:
1.6x + 3 = 21
use inverse operation (+ = -, x = ÷) by taking 3 to the opposite side and changing it's integer to negative
1.6x = 21 - 3
divide 2 sides by 1.6
1.6x = 18
1.6x/1.6 = 18/1.6
x = 11.25//
2.15(x-5)=75
inverse operation
x= 75 - 2.15 + 5
x= 77.85//
Find the general solution of the given second-order differential equation. 12y'' − 5y' − 3y = 0
The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
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Solve:
8(3 + a) = 64
A =
Answer: 8
Step-by-step explanation:
PEMDAS
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Which point is located at (-3.5,-4.5)?
543
J
♦K
R
to
point A
S
(21
te
3
21
..
-3
-5
2 3
#
157
Xb
Answer:
Point A
Step-by-step explanation:
See attached worksheet.
How many times do you need to divide by ten to get from 0.747 to 0.0747?
Answer:
Step-by-step explanation:
Quick Answer 1
Solution
x = 0.747 / 0.0747
When you do the division, you get 10. That means that you need to divide 0.747 by just 1 ten to get 0.0747
Answer:
Once
Step-by-step explanation:
You have to divide once because if you divide a decimal by 10, you add a zero before the decimal point
The measure of angle is 5. The equivalent measurement in degrees is...
Answer:
300 degrees
Step-by-step explanation:
pi should be 180 degrees so 5*180/3 = 5*60=300
pls help ill give brainliest
a=
x=
Answer:
a = 12
x = 5.714
Step-by-step explanation:
sf = 15 / 9
20 / (15 / 9) = 12
a = 12
sf = 21 / 6
20 / (21 / 6)
x = 5.714
Solve the given initial-value problem. y'' 4y' 5y = 35e−4x, y(0) = −5, y'(0) = 1
The solution for the initial value problem is [tex]y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}[/tex]
Given,
y" + 4y' + 5y = 35[tex]e^{-4x}[/tex]
y(0) = -5
y'(0) = 1
Solve this homogenous equation to get [tex]y_{h}[/tex]
According to differential operator theorem,
[tex]y_{h}[/tex] = [tex]e^{ax}[/tex]( A cos (bx) + B sin (bx)), where A and B are constants.
Therefore,
y" + 4y' + 5y = 0
([tex]D^{2}[/tex] + 4D + 5)y = 0
D = -2± i
[tex]y_{h} = e^{-2x} ( A cos (x) + B sin (x))[/tex]
Now, solve for [tex]y_{p}[/tex]
A function of the kind [tex]ce^{-4x}[/tex] is the function on the right, we are trying a solution of the form [tex]y_{p} =ce^{-4x}[/tex], here c is a constant.
[tex]y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}[/tex]
Then the general solution will be like:
[tex]y_{g} =y_{h} +y_{p} \\[/tex]
= [tex]e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}[/tex]
[tex]y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\[/tex]
B = 1 - 24 + 28 = 5
Then the solution for the given initial value problem is
[tex]y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}[/tex]
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Grade 12 Financial Mathematic
n-up Q:
Austin buys a house for R 1 785 000 on the 1st September 2021. The bank gives him an interest rate of
6% p.a. compounded monthly. Mr Austin makes payments of R11 000 at the end of each month.
a) What is the balance on the loan on the 31st December 2036?
b) How long will it take Mr Austin to payoff the loan?
Answer:
a)0.00
b)13year,8month,2weeks and 6day
Select the correct answer from each drop-down menu. B For circle O, m In the figure, 2 C CD T - 125° and m2ABC= 55°. and 2 have measures equal to 35°.
Answer:
Step-by-step explanation:
The relevant relations here are ...
the sum of arc measures in a semicircle is 180°the sum of angles in a triangle is 180°Arc measuresThe given arc CD is part of the semicircular arc CDA. The remaining arc, DA, is the supplement of CD:
arc DA = 180° -CD = 180° -125° = 55°
Central angle AOD has the same measure, 55°. That is one of the acute angles in right triangle AOB, so the other one is the complement of 55°.
∠ABO = 90° -∠AOB = 90° -55°
∠ABO = 35°
Triangle anglesIn right triangle ABC, angle ABC is given as 55°. The other acute angle, ACB, will be the complement of this.
∠ACB = 90° -∠ABC = 90° -55°
∠ACB = 35°
In the figure, angles ABO and ACB have measures of 35°.
Jenny packaged 108 eggs in 9 cartons. Write this statement as a ratio
Answer:
12:1
Step-by-step explanation:
each pack contains 12 eggs
108/9 = 12
Hope this helps
If a doctor charges $500 per hour for her services, how much would it cost to hire this doctor for 45 minutes?
It will cost $375 to hire the doctor for 45 minutes
The doctor charges $500 for an hour
60 minutes makes 1 hour
60 minutes= $500
Therefore the amount that will be charged for 45 minutes can be calculated as follows
60 minutes= $500
45 minutes= x
Cross multiply both sides
60x= 500×45
60x= 22500
x= 22500/60
x= 375
Hence it will cost $375 to hire the doctor for 45 minutes
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Select the correct answer. What is the value of the limit lim x 2 (x^2+3x+1/x^3+x+1) ? A. B. 1 C. D.
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
How to get the value of the limit?
Here we want to get the limit:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1}[/tex]
First, we can try to evaluate directly in x = 2 and see if it does not generate any problem, we will get:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1} = \frac{2^2 + 3*2 + 1}{2^3 + 2 + 1} = 1[/tex]
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
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I need help im bad at math
Answer: 243
Step-by-step explanation:
If you divide the 18 inch by two to get the r, you will get 9. So you should multiple the 3 and the 9 square. So it should be 3x81=243
Profit is the difference between revenue and cost. the revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 30x – 130. the cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. the variable x represents the number of skateboards sold.
Profit function in terms of x = 33x + 390.
What is a profit in business?
In its simplest form, it's the amount left after subtracting your total expenses from your total revenue. The money remaining, your profits, can either be kept in the business and re-invested to finance future growth, or distributed as a draw or dividends to stakeholders.Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial
[tex]2x^{3} + 30x - 130[/tex]
The cost, in dollars, of producing the skateboards can be modeled by
[tex]2x^{3} -3x - 520[/tex]
Profit function = Revenue - cost
= [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]
= 33x + 390
Therefore, profit function in terms of x = 33x + 390
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Which of the following expressions is equivalent to ab² + 6ab + 7a3-14a?
(b + 7)(b + 6)(a²-2)
Ob(b + 6)+7(a²-2)
Oa[b(b + 6) +7(a²-2)]
a[(b + 7)(b + 6) (a²-2)]
Answer:
"a[b(b + 6) +7(a²-2)]" (the third one)
Step-by-step explanation:
What is the solution to the system of equations?
y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4
The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)
EquationThere are different types of equation. Namely;
Linear equationQuadratic equationSimultaneous equationy = 1/2x - 6
x = -4
Substitute x = -4 intoy = 1/2x - 6
y = 1/2(-4) - 6
= -4/2 - 6
= -2 - 6
y = -8
Therefore,
The solution to the system of equations y = 1/2x - 6, x = -4 is x = -4 and y = -8. (x, y) = (-4, -8)
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One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls? a. 29/128 b. 743/1024 c. 4089/4096 d. 11/64
Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
What is the binomial distribution formula?The formula exists:
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
The parameters exists:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
The values of the parameters are: p = 0.5 and n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then
[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]
By using the binomial distribution formula
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
substitute the values in the above equation, we get
[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]
[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]
So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]
[tex]=0.0016+0.0001=0.0017 \\[/tex]
[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]
[tex]=1-0.0017=0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
Therefore, the correct answer is option c. 4089/4096
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Can somebody solve this?
Answer:
MO = 12
PR = 3
Step-by-step explanation:
The perimeter of a triangle is calculated by adding all side lengths up:
The perimeter of triangle MNO is given as 48
The perimeter of triangle PQR is given as 12
The ratio is 1/4 (simplified ratio of 12/48)
we can write the following equation using this information:
[tex]\frac{x+2}{12x} = \frac{1}{4}[/tex]
cross multiply fractions
12x = 4x + 8
subtract 4x from both sides
8x = 8
divide both sides by 8
x = 1
Now to find the measure of side lengths in question we replace x with 1
for MO = 12x
12*1 = 12
for PR = x + 2
1 + 2 = 3
An art gallery wants to display 4 pieces of art in the front window. if there are 8 pieces to choose from, how many distinct displays are possible?
Answer:
70
Step-by-step explanation:
8 choose 4: 8!/(4!*4!)=70
Answer:
1680
Step-by-step explanation:
the order matters so 8P4
. Rashad is conducting an experiment at his high school to see how people feel about the school dress code. 1. Explain how Rashad could collect data to ensure that it is a random sample of the population. 2. Suppose Rashad has collected his data and has organized it in the table below. Create a visual plot of the data in the table by constructing a bar graph. 3. What is the average view of the dress code? How did you come to this conclusion? 4. The dress code will be changed if more than 60% of the school feels like a change is needed. If 40% of this majority agrees on the same change, that will be what is done with the dress code. Will the dress code change? Do we know which option will occur? Be sure to explain your reasoning.
Each sample has an equal chance of being picked as part of the sampling procedure known as random sampling. A randomly selected sample is intended to provide a fair reflection of the entire population.
How should Rashad proceed with the random sampling?Step 1: He should identify and decide which population he wants to study
Step 2: He should decide the size of the sample. He can do this using a sample size calculator.
Step 3: Select the Sample Randomly using:
Lottery technique; orRandom Number Technique.It is to be noted that the lottery and Random Techniques can be manual or computer simulated.
The sample bar graph for the above sample is attached.
What is the average view of the dress code?About 48 Students (boys and girls combined) indicated that the dress code is nice.13 said it wasn't nice6 on the average indicated that there were indifferent. If 40% of this majority agrees on the same change, that will be what is done with the dress code, will the dress code change?40% of 60% is not likely to catalyze a change in the needed change. A more proper percentage should be 90%.
Do we know which option will occur?Based on the figures given, 72% of the students agree that the dress code is nice (that is , it requires not change).
This means that it is highly unlikely that any changes will be made to the dress code soon.
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8. The cost of renting a scooter is $40 plus $4.50 per hours. Abby wants to spend less than $75
on the scooter rental. Write and solve an inequality to find the number of hours she can rent
the scooter.
Answer:
Step-by-step explanation:
4.5x + 40 < 75
4.5x < 35
x<7.7
5. Find the arc length on a circle with radius of 19 feet created by
an angle of 2(pie)/3radians.
19T
O
38
38T
O 19
O None of the above
**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.
Answer: None of above
Step-by-step explanation:
Given formula
S = r θ
S = arc lengthr = radiusθ = angle in radiansGiven information
radius = 19 ft
Angle = 2π / 3
Substitute values into the formula
S = r θ
S = (19) (2π / 3)
Simplify by multiplication
[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
if 1+sin² =3sin *cos, prove that tan = 1 or 1/2
Step-by-step explanation:
hif 1+sin² =3sin *cos, prove that tan = 1 or 1/2Please help!! 100 points
The graph shows a system of inequalities.
Which point is a solution to the system
(-1,6)
(0,22)
(2,9)
(8,2)
Answer: (2,9)
Step-by-step explanation:
The point lies in the region that is shaded by both inequalities.
hich value, when placed in the box, would result in a system of equations with infinitely many solutions?
y = -2x + 4
6x + 3y =
The value placed in the box that makes the system of equation with infinitely many solution is 12.
How to solve an infinitely many solution equation?An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If we simplify the equation we will notice both sides are equal. This means the equation has an infinitely many solution.
Hence,
y = -2x + 4
Therefore,
6x + 3y = 12
divide the equation(ii) by 3
2x + y = 4
y = -2x + 4
Therefore, both equation are equal if the the box is filled with 12. This means for the value placed in the box that makes the system of equation with infinitely many solution is 12.
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An ANOVA procedure is applied to data obtained from four distinct populations. The samples, each comprised of 15 observations, were taken from the four populations. The degrees of freedom for the numerator and denominator for the critical value of F are ________.
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
The samples, each comprised of 15 observations, were taken from the four populations.
How to find the degrees of freedom?The determine the degrees of freedom for the numerator and denominator for the critical value of F is given below:
k = 4
n = 15
Total degree of freedom;
= nk - 1
= 59
For numerator, it is
= k -1
= 4 - 1
= 3
For denominator it is
= T - (k -1 )
= 59 - 3
= 56
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
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A blueprint is 1 in: 12ft. Then width of a building is 48ft. What is the width of the building on the blueprint?
The width on the blueprint is 4 inches.
What is the width of the building on the blueprint?
The blueprint is a scale drawing of the building. A scale drawing is a reduced form in terms of dimensions of an original image / building / object
The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 inch 12 feet. This scale means that 1 inch of the blueprint represents 12 feet of the building.
Width of the building on the blueprint = 48 / 12 = 4 inches
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Li Juan solves the equation below by first squaring both sides of the equation. [tex]\sqrt{3-2w}=w+6[/tex]
What extraneous solution does Li Juan obtain?
Answer:
w = -11
Step-by-step explanation:
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]
[tex] 3 - 2w = w^2 + 12w + 36 [/tex]
[tex] w^2 + 14w + 33 = 0 [/tex]
[tex] (w + 11)(w + 3) = 0 [/tex]
[tex] w + 11 = 0 [/tex] or [tex] w + 3 = 0 [/tex]
[tex] w = -11 [/tex] or [tex] w = -3 [/tex]
When you square both sides of an equation, you must check all solutions for extraneous solutions.
Check w = -11.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]
[tex] \sqrt{3 + 22} = -5 [/tex]
[tex] \sqrt{25} = -5 [/tex]
[tex] 5 = -5 [/tex]
This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.
Check w = -3.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]
[tex] \sqrt{3 + 6} = 3 [/tex]
[tex] \sqrt{9} = 3 [/tex]
[tex] 3 = 3 [/tex]
This is a true statement, so the solution w = -3 is valid.
Answer: w = -11
Two cars raced at a race track. the faster car traveled 20 mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race? distance (mi) rate (mph) time (h) slower car 165 r startfraction 165 over r endfraction faster car 225 r 20 startfraction 225 over r 20 endfraction 55 mph 60 mph 75 mph 130 mph
If the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.
Given that the faster car is travelling 20 mph faster than slower car and when slower car travels 165 miles the faster car travels 225 miles.
We are required to find the speed of slower car and faster car.
let the speed of slower car be x mph.
In this way the speed of faster car be (x+20) mph.
Speed=Distance/ time
We have to first take slower car.
x=165/Time
Time=165/x-----------1
Now by taking faster car.
x+20=225/time
Time=225/(x+20)-------2
From equation 1 an equation 2.
165/x=225/(x+20)
225x=165x+3300
225x-165x=3300
60x=3300
x=55 mph
Faster car=55+20
=75 mph.
Hence if the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.
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Geometry question need help finding the answer.
Answer: 1208.96
Step-by-step explanation:
The volume of the cylinder is [tex](\pi)(4^2)(4)=64\pi[/tex]
The volume of the prism is [tex](6)(12)(14)=1008[/tex]
So, the total volume is [tex]1008+64\pi=\boxed{1208.96}[/tex]
